zlatrz.f - Online Linux Manual Page
Section : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzlatrz.f
SYNOPSIS
Functions/Subroutinessubroutine zlatrz (M, N, L, A, LDA, TAU, WORK)
ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.
Function/Subroutine Documentation
subroutine zlatrz (integer M, integer N, integer L, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( * ) WORK)ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations. Purpose: ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
[ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means
of unitary transformations, where Z is an (M+L)-by-(M+L) unitary
matrix and, R and A1 are M-by-M upper triangular matrices.Parameters: M M is INTEGER
The number of rows of the matrix A. M >= 0.
N N is INTEGER
The number of columns of the matrix A. N >= 0.
L L is INTEGER
The number of columns of the matrix A containing the
meaningful part of the Householder vectors. N-M >= L >= 0.
A A is COMPLEX*16 array, dimension (LDA,N)
On entry, the leading M-by-N upper trapezoidal part of the
array A must contain the matrix to be factorized.
On exit, the leading M-by-M upper triangular part of A
contains the upper triangular matrix R, and elements N-L+1 to
N of the first M rows of A, with the array TAU, represent the
unitary matrix Z as a product of M elementary reflectors.
LDA LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU TAU is COMPLEX*16 array, dimension (M)
The scalar factors of the elementary reflectors.
WORK WORK is COMPLEX*16 array, dimension (M)Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: December 2016 Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA Further Details: The factorization is obtained by Householder's method. The kth
transformation matrix, Z( k ), which is used to introduce zeros into
the ( m - k + 1 )th row of A, is given in the form
Z( k ) = ( I 0 ),
( 0 T( k ) )
where
T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ),
( 0 )
( z( k ) )
tau is a scalar and z( k ) is an l element vector. tau and z( k )
are chosen to annihilate the elements of the kth row of A2.
The scalar tau is returned in the kth element of TAU and the vector
u( k ) in the kth row of A2, such that the elements of z( k ) are
in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
the upper triangular part of A1.
Z is given by
Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).Definition at line 142 of file zlatrz.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
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